Fourier series for a random function

My problem consists of :
there is a representation of an uneven surface in terms of Fourier series with random coefficients:

The random coefficients are under several conditions:

W - function is undefined.

Maybe you've confronted with such kind of expressions.
The question is : how to determine P-coefficients? Maybe they can be presented by means of some well-known probability density distributions or smth with a help of Monte-Carlo numerical methods?